# Fermion-scalar conformal blocks

@article{Iliesiu2015FermionscalarCB,
title={Fermion-scalar conformal blocks},
author={Luca V. Iliesiu and Filip Kos and David Poland and Silviu S. Pufu and David Simmons-Duffin and Ran Yacoby},
journal={Journal of High Energy Physics},
year={2015},
volume={2016},
pages={1-20}
}
• Published 4 November 2015
• Mathematics, Physics
• Journal of High Energy Physics
A bstractWe compute the conformal blocks associated with scalar-scalar-fermion-fermion 4-point functions in 3D CFTs. Together with the known scalar conformal blocks, our result completes the task of determining the so-called ‘seed blocks’ in three dimensions. Conformal blocks associated with 4-point functions of operators with arbitrary spins can now be determined from these seed blocks by using known differential operators.

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## References

SHOWING 1-10 OF 61 REFERENCES

### Bootstrapping 3D fermions

• Physics
• 2015
A bstractWe study the conformal bootstrap for a 4-point function of fermions 〈ψψψψ〉 in 3D. We first introduce an embedding formalism for 3D spinors and compute the conformal blocks appearing in

### Deconstructing conformal blocks in 4D CFT

• Mathematics
• 2015
A bstractWe show how conformal partial waves (or conformal blocks) of spinor/tensor correlators can be related to each other by means of differential operators in four dimensional conformal field

### Recursion relations for conformal blocks

• Mathematics
• 2015
A bstractIn the context of conformal field theories in general space-time dimension, we find all the possible singularities of the conformal blocks as functions of the scaling dimension Δ of the

### Scalar-vector bootstrap

• Mathematics
• 2015
A bstractWe work out all of the details required for implementation of the conformal bootstrap program applied to the four-point function of two scalars and two vectors in an abstract conformal field

### Central charge bounds in 4D conformal field theory

• Computer Science
• 2011
It is shown that the stress tensor central charge C-T is bounded from below by a universal function of the dimensions of the lowest and second-lowest scalars present in the conformal field theory.

### Radial Coordinates for Conformal Blocks

• Mathematics
• 2013
We develop the theory of conformal blocks in CFT_d expressing them as power series with Gegenbauer polynomial coefficients. Such series have a clear physical meaning when the conformal block is

### Projectors, shadows, and conformal blocks

A bstractWe introduce a method for computing conformal blocks of operators in arbitrary Lorentz representations in any spacetime dimension, making it possible to apply bootstrap techniques to

### Bootstrapping the 3d Ising twist defect

• Physics, Mathematics
• 2014
A bstractRecent numerical results point to the existence of a conformally invariant twist defect in the critical 3d Ising model. In this note we show that this fact is supported by both epsilon

### The superconformal bootstrap for structure constants

• Mathematics
• 2014
A bstractWe report on non-perturbative bounds for structure constants on N=4$$\mathcal{N}=4$$ SYM. Such bounds are obtained by applying the conformal bootstrap recently extended to super-conformal

### Bootstrapping the Three Dimensional Supersymmetric Ising Model.

• Physics
Physical review letters
• 2015
The conformal bootstrap program for three dimensional conformal field theories with N=2 supersymmetry is implemented and universal constraints on the spectrum of operator dimensions in these theories are found.